28 Aug 2007 KKKQ 3013 PENGIRAAN BERANGKA Week 8 – Numerical Derivatives & Integrals 28 August 2007...
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Transcript of 28 Aug 2007 KKKQ 3013 PENGIRAAN BERANGKA Week 8 – Numerical Derivatives & Integrals 28 August 2007...
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28 Aug 2007
KKKQ 3013KKKQ 3013PENGIRAAN BERANGKAPENGIRAAN BERANGKA
Week 8 – Numerical Derivatives & Integrals28 August 2007
8.00 am – 9.00 am
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28 Aug 2007 Week 8 Page 2
Topics
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28 Aug 2007 Week 8 Page 3
Tutorial Example 1 (adapted courtesy of ref. [1])
[1] KQ3013 lecture notes
For the following function
f(x) = sin x
a) Apply the first, second and third order Taylor series to predict f(x) at x = /6 with x = 0 as base point. Use step sizes /6, /12 and /18. For each case, determine the true relative error.
b) Evaluate the forward, backward and centred finite divided difference of the function at x = /6 with step sizes /6, /12 and /18. Similarly, for each case, determine the true relative error.
c) Numerically evaluate the integration of the function between x = 0 and using
i. Trapezoidal rule with 4 segments
ii. 1/3-Simpson rule with 4 segments
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Tutorial Example 1
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Tutorial Example 1
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Tutorial Example 1
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Tutorial Example 1
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28 Aug 2007 Week 8 Page 8
Tutorial Example 1
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Tutorial Example 1
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Tutorial Example 1